The slide carried away the house in a heavily wooded area in Bombinasco at around 6.15pm on Wednesday, police said in a statement.
The victims, who were renting the home, were retrieved by searchers including a dog team, fire fighters and police officers, at 4.30am on Thursday, the statement said.
Police said the landslide occurred on a steep slope and wiped out the equivalent of 4,500 cubic metres of wood, mainly from chestnut trees.
Claudio Zali, cantonal minister of lands, said the area was not considered at risk for such an event.
"Things like this should not happen, but we must be aware that extraordinary events such as this can happen," Zali told Italian-language broadcaster RSI.
"We must remember that we live in a mountainous canton and when rainfall is exceptionally heavy, as was the case over these past few days, things like this can happen."
Zali, who went to the location of the slide to observe the start of the rescue operation, passed on his condolences to the victim's family.
He also said that the canton would re-evaluate its method of determining the risk of such events happening elsewhere.
The landslide follows heavy rain in the canton over the past day after a windstorm swept through the Alps earlier this week.
Authorities closed the nearby road between Banco and Astano because of fears of another slide in the area west of Lugano and close to the Italian border.
Meanwhile, in an unrelated incident, cantonal police reported finding two people dead inside a car that caught fire in Mendrisio on Thursday at about 7.30am.
Police said an investigation was under way to identify the victims and found out what happened.